Hosier Lane
Opposite Federation square, is Hosier lane, check out graffiti and the Until Never Gallery, its upstairs and the entrance is in the sidelane
Go to the bar on the corner called Movida for Tapashttp://www.movida.com.au/hosier.html

For Coffee and the place to be seen - Degraves Street - any of the coffee barshttp://www.degravesstreetonline.com
It crosses Flinders Lane this is full of cool boutiques and some of Melbourne's private galleries. Walk across Flinders lane and into Centre Place and from here you can continue on through the arcade to Collins Street

I've marked near Vic Markets the Blender Studios which is an artist space and studios, near there on the corner of Elizabeth and A'Beckett Street there is an upstairs bar if you want coffee or a drink.

If you are feeling arty there are Two National Galleries, both NGV's are good, The NGV Australian Collection in Federation Square - there is a huge information centre here, or the International Collection is at NGV International - they do a fancy afternoon tea with cakes in the UPSTAIRS cafe.